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A theorem of the Wiener—Tauberian type forL 1(H n)

  • Rama Rawat
Article

Abstract

The Heisenberg motion groupHM(n), which is a semi-direct product of the Heisenberg group Hn and the unitary group U(n), acts on Hn in a natural way. Here we prove a Wiener-Tauberian theorem for L1 (Hn) with this HM(n)-action on Hn i.e. we give conditions on the “group theoretic” Fourier transform of a functionf in L1 (Hn) in order that the linear span ofgf : g∈HM(n) is dense in L1(Hn), wheregf(z, t) =f(g·(z, t)), forg ∈ HM(n), (z,t)∈Hn.

Keywords

Heisenberg group Gelfand pairs class-1 representations elementary spherical functions 

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Copyright information

© Indian Academy of Sciences 1996

Authors and Affiliations

  • Rama Rawat
    • 1
  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteBangaloreIndia

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